Randy is correct. The "glass snake" your cousin found is in fact a glass lizard, not related closely to garter snakes and in fact not a snake at all. It may look like a snake superficially, owing to the lack of limbs, but the existence of moveable eyelids and external ear openings means it's a lizard.
The tail, which constitutes at least 2/3rds of the total length when fully intact, is very delicate and in fact is designed to break off easily. This allows the lizard to escape from predators while the predator goes for the still-wriggling tail. The lizard will regenerate a new tail eventually.
The glass reference refers to the fact that glass lizards, while resembling snakes in outward appearance, are much more rigid and less supple overall than snakes. Because of the fact that they are so "brittle" with regard to potential tail breakoff, I generally leave them alone if I encounter them in the field. I recommend releasing it back into the wild.
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MichaelB